Question

In high school, a teacher gave two sections of a class the same arithmetic test. The results were as follows:

Section I: Mean 45, Standard
Deviation 6.5
Section II: Mean 45,
Standard deviation 3.1

What conclusions is correct?

Answer 1

Section I test scores are more dispersed that that of section II.

Explanation:

Consider the data collected from the arithmetic test given to two sections of a school.

Section I: Mean = 45, Standard Deviation = 6.5

Section II: Mean = 45, Standard deviation = 3.1

The mean of both the sections are same, i.e. 45.

So there is no comparison that can be made from the center of the distribution.

The standard deviation for section I is 6.5 and the standard deviation for section II is 3.1.

The standard deviation is a measure of dispersion, i.e. it tells us how dispersed the data is from the mean or how much variability is present in the data.

The standard deviation for section I is higher than that of section II.

So, this implies that section I test scores are more dispersed that that of section II.